Linear-Scaling Systematic Molecular Fragmentation Approach for Perturbation Theory and Coupled-Cluster Methods

The density-based many-body expansion for poly-peptides and proteins

Fragmentation schemes enable the efficient quantum-chemical treatment of large biomolecular systems, and provide an ideal starting point for the development of accurate machine-learning potentials for proteins. Here, we present a fragment-based method that only uses calculations for single-amino acids and their dimers, and is able to reduce the fragmentation error in total energies to ca. 1 kJ mol-1 per amino acid for polypeptides and proteins across different structural motifs. This is achieved by combining a two-body extension of the molecular fractionation with conjugate caps (MFCC) scheme with the density-based many-body expansion (db-MBE), thus extending the applicability of the db-MBE from molecular clusters to polypeptides and proteins.

Protein-Ligand Interaction Energies from Quantum-Chemical Fragmentation Methods: Upgrading the MFCC-Scheme with Many-Body Contributions

Quantum-chemical fragmentation methods offer an attractive approach for the accurate calculation of protein-ligand interaction energies. While the molecular fractionation with conjugate caps (MFCC) scheme offers a rather straightforward approach for this purpose, its accuracy is often not sufficient. Here, we upgrade the MFCC scheme for the calculation of protein-ligand interactions by including many-body contributions. The resulting fragmentation scheme is an extension of our previously developed MFCC-MBE(2) scheme [J. Comput. Chem. 2023, 44, 1634-1644]. For a diverse test set of protein-ligand complexes, we demonstrate that by upgrading the MFCC scheme with many-body contributions, the error in protein-ligand interaction energies can be reduced significantly, and one generally achieves errors below 20 kJ/mol. Our scheme allows for systematically reducing these errors by including higher-order many-body contributions. As it combines the use of single amino acid fragments with high accuracy, our scheme provides an ideal starting point for the parametrization of accurate machine learning potentials for proteins and protein-ligand interactions.

Intermolecular interaction energies with AROFRAG-A systematic approach for fragmentation of aromatic molecules

Intermolecular interactions with polycyclic aromatic hydrocarbons (PAHs) represent an important area of physisorption studies. These investigations are often hampered by a size of interacting PAHs, which makes the calculation prohibitively expensive. Therefore, methods designed to deal with large molecules could be helpful to reduce the computational costs of such studies. Recently we have introduced a new systematic approach for the molecular fragmentation of PAHs, denoted as AROFRAG, which decomposes a large PAH molecule into a set of predefined small PAHs with a benzene ring being the smallest unbreakable unit, and which in conjunction with the Molecules-in-Molecules (MIM) approach provides an accurate description of total molecular energies. In this contribution we propose an extension of the AROFRAG, which provides a description of intermolecular interactions for complexes composed of PAH molecules. The examination of interaction energy partitioning for various test cases shows that the AROFRAG3 model connected with the MIM approach accurately reproduces all important components of the interaction energy. An additional important finding in our study is that the computationally expensive long-range electron-correlation part of the interaction energy, that is, the dispersion component, is well described at lower AROFRAG levels even without MIM, which makes the latter models interesting alternatives to existing methods for an accurate description of the electron-correlated part of the interaction energy.

Cluster-in-Cluster Approach for Computing MP2-Level Vibrational Infrared Spectra of Large Molecular Clusters

Constructing the Hessian matrix (HM) for large molecules demands huge computational resources. Here, we report a cluster-in-cluster (CIC) procedure for efficiently evaluating HM and dipole derivatives for large molecular clusters by employing the second-order Møller-Plesset perturbation (MP2) theory. The highlight of the proposal is the separation of the estimations of Hartree-Fock (HF) and post-HF components. The parent cluster with n molecules is divided (virtually) into n subclusters centering each monomer and accommodating its near neighbors decided by a distance cutoff. The HF-level HM is obtained by doing full calculation (FC), while the correlation part is approximated by the respective subclusters. A software automating the procedure [followed by calculating infrared (IR) frequencies and intensities] is applied to deduce the IR spectrum for a variety of molecular clusters, particularly water clusters of various sizes, containing up to ∼2000 basis functions. The accuracy of the IR spectrum constructed using CIC is remarkable, with a substantial time advantage (with respect to its FC counterpart). The reduced computational resources and the tractability of the computations are other major benefits of the procedure.

AROFRAG─A Systematic Approach for Fragmentation of Aromatic Molecules

We present a new systematic fragmentation scheme of polycyclic aromatic hydrocarbons (PAHs), including fullerenes and nanotubes, based on an idea to treat a sextet ring as a single unbreakable unit so that the basic unit of aromaticity remains preserved upon fragmentation. In the approach, denoted as AROFRAG (from aromatic fragmentation), a set of predefined elementary subsystems, such as naphthalene and biphenyl in the first model and larger PAHs in the second and third models, is generated with appropriate weights with the aim of reproducing the structure of the original molecule. The energies of the molecules are approximated as weighted sums of the energies of these subsystems. For symmetric cases, e.g., fullerenes, the point-group symmetry is preserved during the decomposition. The AROFRAG is used in conjunction with the molecule-in-molecule (MIM) technique to obtain an accurate description of the electronic energies. The new approach has been applied for selected graphene structures and fullerene doped with boron and nitrogen atoms, for which isomerization energies were calculated, as well as for several nanotubes and regular fullerene molecules. The combination of the third AROFRAG model and the MIM approach leads to the reproduction of electronic energies with a few milli-hartree accuracy at a fraction of the computational cost of the original method.

Massively parallel implementation of gradients within the random phase approximation: Application to the polymorphs of benzene

The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars.

REAlgo: Rapid and efficient algorithm for estimating MP2/CCSD energy gradients for large molecular clusters

This work reports the development of an algorithm for rapid and efficient evaluation of energy gradients for large molecular clusters employing correlated methods viz. second-order Møller-Plesset perturbation theory (MP2) theory and couple cluster singles and doubles (CCSD). The procedure segregates the estimation of Hartree-Fock (HF) and correlation components. The HF energy and gradients are obtained by performing a full calculation. The correlation energy is approximated as the corresponding two-body interaction energy. Correlation gradients for each monomer are approximated from the respective monomer-centric fragments comprising its immediate neighbours. The programmed algorithm is explored for the geometry optimization of large molecular clusters using the BERNY optimizer as implemented in the Gaussian suite of software. The accuracy and efficacy of the method are critically probed for a variety of large molecular clusters containing up to 3000 basis functions, in particular large water clusters. The CCSD level geometry optimization of molecular clusters containing ∼800 basis functions employing a modest hardware is also reported.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.